This is certainly a development to keep an eye on, as it could lead to complications for EU organizations doing business in the UK or having other UK ties.
Short term: Basically nothing. The UK will need to comply with the Regulation while it is still a part of the EU.
Long term: Will possibly become a “third country” in terms of data transfers. Once the UK leaves the EU, the GDPR will still have an impact. Firstly, the regulation applies to all companies based in the EU and those with EU citizens as customers. Therefore, UK companies continuing to do business with the EU after Brexit will still need to comply with the Regulation. Secondly, the GDPR has raised awareness regarding data protection. Considering the high level of international business involving the EU, the GDPR is likely to influence stronger data protection procedures around the world. It is therefore unlikely that future UK data protection legislation and guidelines will deviate in any significant way from the GDPR.
However, it is still uncertain whether the EU will consider the UK to have an “adequate protection level” in the meaning of GDPR article 47. If not, it will not be possible for EU organizations to transfer data to organizations within the UK unless strict conditions are in place. This is certainly a development to keep an eye on, as it could lead to complications for EU organizations doing business in the UK or having other UK ties.